Lion-tamer with enormous bird of prey sleeps only occasionally (9)
I believe the answer is:
androcles
'lion-tamer' is the definition.
(man who tamed a lion in folklore)
'with enormous bird of prey sleeps only occasionally' is the wordplay.
'with' becomes 'and'.
'enormous bird of prey' becomes 'roc' (mythical giant bird).
'only occasionally' indicates alternate letters (letters taken at regular intervals or occasions).
The alternate letters of 'sleeps' are 'les'.
'and'+'roc'+'les'='ANDROCLES'
(Other definitions for androcles that I've seen before include "Shaw play: -- and the Lion" , "He played a lion-tamer" .)